I’ve not really tried growing anything over winter before, but saw some reasonably priced onion sets a couple of weeks ago.

They were a Japanese variety, specially suited to surviving our cold winter. And here they are, two weeks after planting and starting to shoot. That tells me that they’re putting out roots under the soil, which will serve them well during the coldest months.
So long as they don’t bolt/go to seed, I should get a nice crop come next spring or early summer, long before spring-planted sets are ready.